Trade unionists have called for Royal Mail to take legal action if its mandate to deliver to even the most remote homes in the UK comes under threat.

Members of the Communication Workers Union (CWU) voiced fears about competition from the rival carrier TNT at Royal Mail's first annual shareholder meeting in Birmingham. Around 150 employees, union representatives, pensioners and stamp collectors gathered at the National Exhibition Centre, where the atmosphere was subdued as chief executive Moya Greene and her board mingled with shareholders over tea and biscuits, in rooms dotted with replica post boxes.

With little sign of the trench warfare between unions and management that preceded October's privatisation, more than 95% of all votes, including abstentions, were in favour of the remuneration policy, 98% backed the rewards collected by executives in the most recent financial year, including Greene's £1.35m package, and 96% approved to the long term incentive scheme.

Chairman Donald Brydon, who was criticised by the shareholder advisory group PIRC for chairing two FTSE companies – he also heads the board at Sage – drew nearly 5m protest votes but his re-election was approved with a 98% majority.

Unions, however, have joined Greene in pushing for a rethink of how rivals such as TNT compete with the Royal Mail in delivering mail to the doorstep. In June Royal Mail asked its regulator, Ofcom, to bring forward a planned review of the effects of rival doorstep deliveries to this year, but it has yet to receive an answer.

A group of CWU representatives in London, where competition with TNT is most fierce, is now pushing for a judicial review if Ofcom decides not to bring forward its investigation. "As Ofcom do not appear to be listening to the company, is there any prospect of the company calling for a judicial review over the impact of the direct delivery competition?" Ian Murphy, the CMU's regional secretary for London asked during shareholder questions.

The chairman did not rule out taking action if Ofcom boss Ed Richards failed to. "It's important that there is a review of practices in the market as quickly as possible," Brydon said. "I think we need to find out how Ofcom will proceed before we can conclude as to whether we will take further steps at a later point, but you can believe that a huge amount of our energy is being put into the argument … and the need to preserve the universal service is absolutely front of mind and one of the major actions in the company at this time."

TNT, the Royal Mail's main competitor for British home deliveries, has contributed to a 20% fall in volumes in certain areas including south-west London, according to the CWU. The company began doorstep mail delivery in London in 2012 and has since expanded to Manchester and Liverpool, with Birmingham and Bristol understood to be next in line.

A spokesman for Ofcom said: "Protecting the universal service is at the heart of Ofcom's work, and we are currently considering a report Royal Mail has given us regarding competition in the market." The regulator said it was actively monitoring competition and could impose a "universal service condition" on all doorstep delivery companies if necessary.

Greene told shareholders: "When you post a first class letter we charge you the same to deliver it tomorrow in Solihull or in John O'Groats. We can do this only if we can use the money we make in the easy-to-serve urban areas to pay the higher cost of deliver to rural and suburban areas. Ofcom's primary duty is to secure the sustainability of the universal service. So, we have asked the regulator to review this situation right away."

Royal Mail's warnings on competition sent shares into a tailspin in May, and the stock fell to new lows this week when Greene revealed the previously fast growing parcels business had seen revenue fall 1% in the quarter ending in June. She blamed the drop on Amazon's decision to charge postage on orders under £10, the online retailer's growing network of delivery drivers and Royal Mail's decision to avoid carrying parcels that cannot be transported on foot.

Parcel sizes are also responsible for a decline in bicycle deliveries. With postmen increasingly opting for vans or trolleys on the majority of the UK's 80,000 rounds, Brydon fondly recalled his own postman as a child doing his rounds on two wheels. But he warned: "Bicycle deliveries for this company are going to be a thing of the past."